Yeah, I do the same recording and replicating of player inputs ¦3
What I discovered was that to make it consistently reproducible, I had to somehow tie each input to a specific step of the physics simulation. And then having physics calculation at a fixed rate allowed me to use the count of such physical steps as a pretty solid measure of time for inputs (e.g. if I repeat the "jump" action exactly at step 119 every time, the end result will be exactly the same, if the surrounding world hasn't changed).
However, in your case, with all the moving platforms that would not work, as in the next run you can change the configuration of walls, making previous enemies hit them as they move, changing the result of their movement.
So that's a pretty hard task ¦3